The infected woman had visited the Dominican Republic and she was now in satisfactory condition in an infectious diseases hospital, Rospotrebnadzor said in a statement, Xinhua reported.
"Medical observation of family members was established. No clinical manifestations of the virus were registered among them, and they tested negative for the Zika virus," the statement said.
Precautionary measures were taken in regard to the passenger plane on which the infected Russian citizen flew home, and there was no threat to the health of other passengers, it added.
Rospotrebnadzor started weekly monitor of individuals coming from countries troubled by vector-borne infections since the beginning of 2016.
Russia enhanced inspection measures on Monday as over 50,000 people were checked at airports and sea border crossing points for signs of infectious diseases, the public health watchdog said.
Russian Health Minister Veronika Skvortsova confirmed that "all aircraft and ships arriving from 21 countries affected by Zika are disinfected and all passengers are checked onboard before entering Russia".
Russian doctors have prepared methodological recommendations on diagnosing and treatment, she was quoted by Tass news agency.
Noting that Zika is not likely to spread considering the climate conditions of Russia, Rospotrebnadzor said the situation remains under control.
The agency warned Russians of visiting tropical or subtropical countries troubled by epidemic diseases, noticing such symptoms of the Zika virus as fever, a rash, conjunctivitis, joint and muscle pain, headache and fatigue.
Transmitted by mosquitoes, the Zika virus is suspected of causing infected pregnant women to give birth to babies with microcephaly.
The Zika outbreak has reportedly affected more than 30 countries, and the World Health Organisation said on Friday that possible Zika vaccines were expected to come out for large-scale clinical trials in at least 18 months.